Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses at the restaurant? (Assume that all boxes are filled to capacity.)

1. 96
2. 240
3. 256
4. 384
5. 480

Correct Answer: E
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:

• At a restaurant, glasses are stored in two different-sized boxes.
• One box contains 12 glasses, and the other contains 16 glasses.
• If the average number of glasses per box is 15, there are 16 more of the larger boxes.

Find out:

• The total number of glasses at the restaurant.

Let the number of boxes holding 12 glasses each be x and those holding 16 be y.
Thus, \({(12 ∗ x + 16 ∗ y)\over (x + y) }=15\) 
=> 12x + 16y = 15x + 15y
=> 16y - 15y = 15x - 12x
=> y = 3x …. (i)
Again from the given conditions of the question, we know that:
y = x + 16 …..(ii)
By simplifying both equations we get:
x + 16 = 3x
=> 2x = 16
=> x = 8
Therefore, y = 3 * 8 = 24.
Hence, the total number of glasses = (x+y) * 15
= (8 + 24) * 15
= 32*15
= 480.

Approach Solution 2:
The problem statement implies that:
Given:

• At a restaurant, glasses are stored in two different-sized boxes.
• One box contains 12 glasses, and the other contains 16 glasses.
• If the average number of glasses per box is 15, there are 16 more of the larger boxes.

Find out:

• The total number of glasses at the restaurant.

Since the question states that there are 16 more of the larger boxes.
This implies that at the minimum, we hold:
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can eliminate Options A, B and C.
The difference in the number of boxes must be 16.
Therefore we could have:
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes etc.
With every additional small box + large box that we add, we count 12+16 = 28 more glasses. Therefore, we can just “add 28s” until we get the correct answer.
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we have gone behind option D, therefore, the correct answer must be option E.
So let’s evaluate further:
396+28 = 424
424+28 = 452
452+28 = 480
Hence, the total number of glasses = 480 i.e correct answer is option E.

Approach Solution 3:
The problem statement states that:
Given:

• At a restaurant, glasses are stored in two different-sized boxes.
• One box contains 12 glasses, and the other contains 16 glasses.
• If the average number of glasses per box is 15, there are 16 more of the larger boxes.

Find out:

• The total number of glasses at the restaurant

Let’s solve the problem by using the alligation method
\(\frac{W1}{W2}=\frac{A2-Avg}{Avg-A1}\)
There are 16 more of the larger boxes. This implies x + 16 = W2
W1 = x
A1 = 12
A2 = 16
Avg = 15
By simplifying the equation \(\frac{W1}{W2}=\frac{A2-Avg}{Avg-A1}\), we get:
=> \(\frac{x}{x+16}=\frac{16-15}{15-12}\)
=> \(\frac{x}{x+16}=\frac{1}{3}\)
=> 3x = x + 16
=> 2x = 16
=> x = 8
Therefore, the total number of glasses in the smaller box = 8 * 12 = 96 glasses
Therefore, the total number of boxes in the larger box (x + 16) = 24 * 16 = 384 Glasses
Hence, the total number of glasses at the restaurant = 96 + 384 = 480.

“At a restaurant, glasses are stored in two different-sized boxes”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book GMAT Prep Plus 2021. The candidates must analyse the facts given in the GMAT Problem Solving questions to interpret numerical problems. GMAT Quant practice papers help the candidates to go through different types of questions that will enable them to strengthen their mathematical knowledge.

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